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Let n be in N and let K be a field. Show that for a linear...

Let n be in N and let K be a field. Show that for a linear map T : Kn to Kn the following statements are equivalent:

1. The map T is one-to-one (injective).

2. The map T is onto (surjective).

3. The map T is invertible.

4. The map T is an isomorphism.

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